From ms8a017 at math.uni-hamburg.de  Tue Dec  9 21:44:34 2003
From: ms8a017 at math.uni-hamburg.de (Hubert Kiechle)
Date: Fri Apr  8 15:25:37 2005
Subject: [GAP Forum] InstallMethod
Message-ID: <Pine.GSO.3.95q.1031209224238.28538A-100000@sun35.math.uni-hamburg.de>

Hi GAP-forum,

I want to invert 2x2 matrices over a (finite) algebra with zero
divisors. As there does not seem to be a method available, I tried to
provide one, but the following file
after *Read*ing into gap leads to the ERROR message below which seems
cryptic to me. In fact, after *return*ing from the break loop
*Inverse* works perfectly well.

How can I get rid of the ERROR message?
Why is there no method for *Inverse* in matrix rings over rings with
zero divisors?


-----  file ----
Inv22:=function(m)
  local  u;
  if DimensionsMat(m)=[2,2] then
    u:=Determinant(m);
    if IsUnit(u) then
      return Inverse(u)*[[m[2][2],-m[1][2]],[-m[2][1],m[1][1]]];
    else 
      return fail;
    fi;
  else
    return fail;
  fi;
end;

InstallMethod( Inverse,
        "Inverse of 2x2 Matrix over any Ring",
        [IsMatrix and IsRingElementCollColl],Inv22);

---------
Error, required filters [ "IS_LIST", "IS_DENSE_LIST", "IS_HOMOG_LIST", 
  "IS_TABLE_LIST", "IsListOrCollection", "IsCollection", "IsExtAElement", 
  "CategoryCollections(IsExtAElement)", 
  "IsNearAdditiveElement", "CategoryCollections(IsNearAdditiveElement)", 
  "CategoryCollections(CategoryCollections(IsNearAdditiveElement))", 
  "IsNearAdditiveElementWithZero", 
  "CategoryCollections(IsNearAdditiveElementWithZero)", 

"CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))", 
  "IsNearAdditiveElementWithInverse", 
  "CategoryCollections(IsNearAdditiveElementWithInverse)", 

"CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))"
    , "IsAdditiveElement", "CategoryCollections(IsAdditiveElement)", 
  "CategoryCollections(CategoryCollections(IsAdditiveElement))", 
  "IsExtLElement", "CategoryCollections(IsExtLElement)", 
  "CategoryCollections(CategoryCollections(IsExtLElement))",
"IsExtRElement", 
  "CategoryCollections(IsExtRElement)", 
  "CategoryCollections(CategoryCollections(IsExtRElement))", 
  "IsMultiplicativeElement", 
  "CategoryCollections(CategoryCollections(IsMultiplicativeElement))", 
  "IsGeneralizedRowVector" ]
for 1st argument do not match a declaration of InverseImmutable called
from
<compiled or corrupted call value>  called from
<function>( <arguments> ) called from read-eval-loop


Thanks for any help,

Hubert

* Priv. Doz. Dr. Hubert Kiechle *
*                               *
* Mathematisches Seminar        *
* Universität Hamburg           *   Outside of a dog,
* Bundesstr. 55                 *     a book is man's best friend.
* D-20146 Hamburg               *   Inside of a dog,
* Germany                       *     it is too dark to read.
*                               *
* Tel.: +49 40 42838 5186       *
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
http://www.math.uni-hamburg.de/home/kiechle/



From kohl at mathematik.uni-stuttgart.de  Wed Dec 10 09:55:02 2003
From: kohl at mathematik.uni-stuttgart.de (Stefan Kohl)
Date: Fri Apr  8 15:25:37 2005
Subject: [GAP Forum] InstallMethod
References: <Pine.GSO.3.95q.1031209224238.28538A-100000@sun35.math.uni-hamburg.de>
Message-ID: <3FD6ED76.DD513B6F@mathematik.uni-stuttgart.de>

Dear Forum,

Hubert Kiechle wrote:

> I want to invert 2x2 matrices over a (finite) algebra with zero
> divisors. As there does not seem to be a method available, I tried to
> provide one, but the following file
> after *Read*ing into gap leads to the ERROR message below which seems
> cryptic to me. In fact, after *return*ing from the break loop
> *Inverse* works perfectly well.
>
> How can I get rid of the ERROR message?
> Why is there no method for *Inverse* in matrix rings over rings with
> zero divisors?
>
> -----  file ----
> Inv22:=function(m)
>   local  u;
>   if DimensionsMat(m)=[2,2] then
>     u:=Determinant(m);
>     if IsUnit(u) then
>       return Inverse(u)*[[m[2][2],-m[1][2]],[-m[2][1],m[1][1]]];
>     else
>       return fail;
>     fi;
>   else
>     return fail;
>   fi;
> end;
>
> InstallMethod( Inverse,
>         "Inverse of 2x2 Matrix over any Ring",
>         [IsMatrix and IsRingElementCollColl],Inv22);
>
> ---------
> Error, required filters [ "IS_LIST", "IS_DENSE_LIST", "IS_HOMOG_LIST",

[ ... ]

The reason for the error message you got is that `InstallMethod' checks
whether the required filters of your method match the declaration of
the attribute `InverseImmutable', for which `Inverse' is a synonym.

You can find these declarations in lib/arith.gd:

   DeclareAttribute( "InverseImmutable", IsMultiplicativeElementWithInverse );
   DeclareSynonymAttr( "Inverse", InverseImmutable );

In your case, the requirement `IsMatrix and IsRingElementCollColl' does not
imply the filter `IsMultiplicativeElementWithInverse' (as there are also non-invertible
matrices), although the attribute `InverseImmutable' is only declared for such
`multiplicative elements with inverse'.

You can circumvent these strict checks by using `InstallOtherMethod' instead of
`InstallMethod'.

In any case you should issue `TryNextMethod();' instead of returning `fail'
in case your matrix is not 2x2 -- otherwise you likely break other functionality,
in particular you might run into trouble when trying to invert matrices larger
than 2x2 after your method installation. This will happen whenever the
method selection ranks your method highest.

You might also think about whether you want to get a mutable or an immutable
result (see the reference manual for a description of mutability / immutability) --
in the former case you should install your method for `InverseMutable',
and in the latter case you should return an immutable object.

Hope this helps,

    Stefan Kohl



From costanti at science.unitn.it  Fri Dec 12 16:52:29 2003
From: costanti at science.unitn.it (Marco Costantini)
Date: Fri Apr  8 15:25:37 2005
Subject: [GAP Forum] The GAP interface to the Singular system
Message-ID: <1071247949.3fd9f24dcd3a8@www.unitn.it>

Dear GAP Forum, 
 
With this message we would like to draw your attention to 
the new version of the GAP interface to the Singular system, 
which has just become available. 
Features of this interface include: 
 
     * fast computation of Groebner bases, 
     * computation of multivariate Gcd, 
     * factorization of multivariate polynomials, 
     * computation of invariant rings of finite groups. 
 
The interface can be downloaded from 
http://www-math.science.unitn.it/~costanti 
 
More information on Singular can be found on 
http://www.singular.uni-kl.de (where the system 
can also be downloaded for free). 
 
If you have any questions please feel free to contact us. 
 
Best wishes, 
 
 
Marco Costantini (costanti@science.unitn.it) 
Willem de Graaf (quagroup@hetnet.nl) 
 
 

From primoz.moravec at fmf.uni-lj.si  Tue Dec 16 16:35:00 2003
From: primoz.moravec at fmf.uni-lj.si (Primoz Moravec)
Date: Fri Apr  8 15:25:38 2005
Subject: [GAP Forum] Low index normal subgroups
Message-ID: <3.0.5.32.20031216173500.00b646e8@fmf.uni-lj.si>

Dear GAP Forum,

what is the best way to compute normal subgroups of low index in a given
finitely presented group?

Best Regards,
Primoz.


------------------------------------
Primoz Moravec
Institute of mathematics, physics
and mechanics
Jadranska 19
SI-1000 Ljubljana
Slovenia

email: primoz.moravec@fmf.uni-lj.si
------------------------------------

From p.dobcsanyi at designtheory.org  Wed Dec 17 11:06:49 2003
From: p.dobcsanyi at designtheory.org (Peter Dobcsanyi)
Date: Fri Apr  8 15:25:38 2005
Subject: [GAP Forum] 'Releases from DesignTheory.org'
Message-ID: <E1AWZVx-0002Ar-00@www.designtheory.org>

            Release Announcements from DesignTheory.org
            ===========================================

The EPSRC funded DesignTheory.org project, based at Queen Mary,
University of London, is pleased to announce the public releases of its
XML-format for block designs and its Design package for GAP.  We expect
these releases to be of interest to those working in combinatorial or
statistical design theory, as well as those interested in the
development of standard electronic formats for mathematical objects.

1)
        The External Representation of Block Designs v1.1,
        http://designtheory.org/library/extrep/

This is a platform independent XML-format for encoding block designs,
and their combinatorial, group-theoretical and statistical properties.

Comments, questions, bug reports -->  extrep@designtheory.org

2)
        Design v1.0 Package for GAP v4.3,
        http://designtheory.org/software/gap_design/

This GAP v4.3 package is for the classification, partitioning and study
of block designs (which include but are not restricted to t-designs).
This package can also write and read block designs in our External
Representation XML-format.

Comments, questions, bug reports -->  gap-design@designtheory.org


Please feel free to forward this announcement to anyone
you think may be interested.

Enjoy,
    The Developers

From costanti at science.unitn.it  Wed Dec 17 14:44:49 2003
From: costanti at science.unitn.it (Marco Costantini)
Date: Fri Apr  8 15:25:38 2005
Subject: [GAP Forum] Low index normal subgroups
In-Reply-To: <3.0.5.32.20031216173500.00b646e8@fmf.uni-lj.si>
References: <3.0.5.32.20031216173500.00b646e8@fmf.uni-lj.si>
Message-ID: <1071672289.3fe06be17b5a6@www.unitn.it>

Dear Primoz and dear gap forum, 
 
Scrive Primoz Moravec <primoz.moravec@fmf.uni-lj.si>: 
> what is the best way to compute normal subgroups of low index in a given 
> finitely presented group? 
 
(I don't know the best way but I can suggest a way to try.) 
 
Look at the functions in the manual in the paragraph Groups - Sets of 
Subgroups: maybe the functions MaximalNormalSubgroups or NormalSubgroups are 
what you need. 
 
Such functions may not terminate in the case that your group is not finite... 
in this case, and if it make sense for your problem, you can consider some 
finite quotient of your group, and calculate MaximalNormalSubgroups or 
NormalSubgroups in it.  
 
There are package to calculare the p-/nilpotent/polyciclic/solvable quotients 
of finitely presented groups (see the packages anupq, nq, etc.). the kind of 
quotient to calculate depends on your problem. 
 
If otherwise your finitely presented group G is finite, it could be better to 
convert it into a polycyclic or permutation group, for efficiency, before 
doing any other computation. 
 
Image(IsomorphismSpecialPcGroup(G));  (if G is solvable) 
Image(IsomorphismPermGroup(G));       (otherwise) 
 
Best Regards, 
Marco 

From hulpke at math.colostate.edu  Wed Dec 17 22:58:47 2003
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Fri Apr  8 15:25:38 2005
Subject: [GAP Forum] Low index normal subgroups
In-Reply-To: <3.0.5.32.20031216173500.00b646e8@fmf.uni-lj.si>
Message-ID: <200312172258.hBHMwlmp016877@schur.math.colostate.edu>

Dear Gap Forum,

Primoz Moravec asked:

> what is the best way to compute normal subgroups of low index in a given
> finitely presented group?

As Marco costatini already pointed out, the methods will be quite different
if you know that the group is finite (``finite'' here probably means: 
order <10^15 ).

If the group is finite, the best approach is to convert to a permutation
group or pc group and use for example `NormalSubgroups'.


If the group is potentially infinite or very large, this might be impossible
or infeasible. In this case I would do the following (assuming again that
your ``small index'' is really small, say up to n=1000:

Using the library of small groups of order <=n (these are the potential
factor groups), determine
- For all solvable groups of order <= n the orders of chief factors. You can
  use these as input to the solvable quotient algorithm to obtain a large
  finite solvable quotient of your group which has all solvable factor
  groups as factors.

- For each nonsolvable group $G$ determine a series of subgroups U1>...>Uk
  such that the image of the action of G on the cosets of Ui is nonsolvable
  and that the action on the cosets of Uk is faithful (often only one
  subgroup suffices, but for groups such as 2.A6 you might want to take a
  subgroup of inder 6 for U1). Then using `LowIndexSubgroups' determine all
  subgroups of the finitely presented group of index $[G:U1]$. Check whether
  the action on the cosets is permutation isomorphic to the action of G on
  the cosets of U1 (for example using `TransitiveIdentification' if the
  index is <=30).
  If U\le F is such a subgroup with [F:U]=[G:U1] determine subgroups of
  index [U1:U2] in U by the low index algorithm. Again compare the types of
  factor groups.
  Iterate until Uk (if not ruled out).

Most nonsolvable groups of large order have a small-degree permutation
representation or a factror group with a low-degree permutation
representation. Thus the second step of this program is probably
comparatively little work.

Best regards,

  Alexander Hulpke

-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke@math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke


From jjoao at netcabo.pt  Tue Dec 30 10:24:49 2003
From: jjoao at netcabo.pt (Jose Joao Morais)
Date: Fri Apr  8 15:25:38 2005
Subject: [GAP Forum] Tuple attribute
Message-ID: <1072779925.4368.6.camel@a213-22-130-67.netcabo.pt>

Dear GAP Forum,

	I have defined an attribute (SemiDirectProductElmAction) for certain
tuples (elements of a semidirect product semigroup being constructed)
because I need to know this attribute to multiply elements of this new
semigroup, but it is not stored when I do

Setter(SemiDirectProductElmAction)(t, act);

	where "t" is the tuple and "act" an action.

	My question is: how can I store this attribute on each of these tuples?


	Thank you,
	Jose Morais


From jjoao at netcabo.pt  Tue Dec 30 10:53:38 2003
From: jjoao at netcabo.pt (Jose Joao Morais)
Date: Fri Apr  8 15:25:38 2005
Subject: [GAP Forum] Tuple attribute
Message-ID: <1072781653.4368.10.camel@a213-22-130-67.netcabo.pt>

Dear GAP Forum,

	I have defined an attribute (SemiDirectProductElmAction) for certain
tuples (elements of a semidirect product semigroup being constructed)
because I need to know this attribute to multiply elements of this new
semigroup, but it is not stored when I do

Setter(SemiDirectProductElmAction)(t, act);

	where "t" is the tuple and "act" an action.

	My question is: how can I store this attribute on each of these tuples?

	Sorry for using the list's old email address, but I got an "Out of
office" reply when sending to the new email address.


	Thank you,
	Jose Morais


From hulpke at math.colostate.edu  Wed Dec 31 00:07:49 2003
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Fri Apr  8 15:25:38 2005
Subject: [GAP Forum] Tuple attribute
In-Reply-To: <1072779925.4368.6.camel@a213-22-130-67.netcabo.pt>
Message-ID: <200312310007.hBV07nJT022376@schur.math.colostate.edu>

Dear GAP Forum,

Jose Morais asked:

>	I have defined an attribute (SemiDirectProductElmAction) for certain
>tuples (elements of a semidirect product semigroup being constructed)
>because I need to know this attribute to multiply elements of this new
>semigroup, but it is not stored when I do

Attributes are only stored if the representation is in
`IsAttributeStoringRep'. Tuples are not in this representation and thus do
not store attributes (which is the behaviour you observed).
To get around the problem there are two ways: the first is to create your
own tuples that use the `ComponentObject' representation and thus are able
to store attributes. In your case however this looks like overkill.

What I would do instead (and is the way similar situations are dealt with in
the library) is to declare the attribute for the *family* of tuples (which
is by default attribute storing):

DeclareAttribute("MyAttribute",IsFamily);

and set this attribute once you create your initial objects:

...
# create generating tuples
tups:=....
fam:=FamilyObj(tups[1]);
SetMyAttribute(fam,actioninfo);

In your multiplication routine (when you need the attribute value) you can
then get it from the family:

MyMultiplication:=function(a,b)
local actioninfo;
  actioninfo:=MyAttribute(FamilyObj(a));

Setter(SemiDirectProductElmAction)(t, act);

(You can see examples of such code in the library file `gprd.gi' that
implements generic products for groups.)

Best wishes and a Happy New Year,

   Alexander Hulpke


-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke@math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke

From jjoao at netcabo.pt  Wed Dec 31 10:47:32 2003
From: jjoao at netcabo.pt (Jose Joao Morais)
Date: Fri Apr  8 15:25:38 2005
Subject: [GAP Forum] Tuple attribute
In-Reply-To: <200312310007.hBV07nJT022376@schur.math.colostate.edu>
References: <200312310007.hBV07nJT022376@schur.math.colostate.edu>
Message-ID: <1072867685.4360.20.camel@localhost.localdomain>

Dear GAP Forum,

	Thank you for your reply to my question about a Tuple attribute.
	While I hadn't your answer, I implemented a new GAP object (Pair) which
is in `IsAttributeStoringRep', but I am having difficulties in defining
a method for the 'ONE' operation applicable to this new object.

gap> p:=Pair(Transformation( [ 1, 2, 3, 4 ] ), Transformation( [ 2, 3,
4, 4 ] ));
Pair(Transformation( [ 1, 2, 3, 4 ] ), Transformation( [ 2, 3, 4, 4 ] ))

gap> Monoid(p);
Error, no method found! For debugging hints type ?Recovery from
NoMethodFound
Error, no 2nd choice method found for `ONE' on 1 arguments called from
OneOp( elm ) called from
One( Representative( M ) ) called from
One( M ) called from
<compiled or corrupted call value>  called from
<compiled or corrupted call value>  called from
...
	

	So, I defined this method:

InstallMethod( OneOp,
        "for pairs",
        true,
        [ IsPair ], 0,
    function( el )
    
    return(Pair(One(el!.first), One(el!.second)));
end );


	but I get the error:

Error, required filters [ "IsPair" ]
for 1st argument do not match a declaration of ONE called from


	Looking then at the declaration of ONE I found:

basicim.gd:210:DeclareOperation( "ONE", [ IsBasicImageEltRep ] );

	
	I have this definition for pairs:

BindGlobal( "PairsType",    NewType( PairsFamily, IsPair and
        IsExtAElement and IsNearAdditiveElement and IsAdditiveElement
and
        IsNearAdditiveElementWithZero and IsAdditiveElementWithZero and
        IsNearAdditiveElementWithInverse and
IsAdditiveElementWithInverse and
        IsAdditivelyCommutativeElement and
        
        CanEasilySortElements and CanEasilySortElements and
        
        IsExtRElement and IsExtLElement and IsMultiplicativeElement and
        IsMultiplicativeElementWithOne and
IsMultiplicativeElementWithZero and
        IsMultiplicativeElementWithInverse and
        IsAssociativeElement and
        IsAttributeStoringRep ));


	but if I add to these filters 'IsBasicImageEltRep', then, when I try to
define a pair I get an error:

gap> p:=Pair(Transformation( [ 1, 2, 3, 4 ] ), Transformation( [ 2, 3,
4, 4 ] ));
Record: '<rec>.Word' must have an assigned value at
return elt!.Word;
 called from
Word( elt ) called from
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop ...


	My question is: how can I define a Pair in such a way that it becomes
suitable for all the operations applicable to Tuples?


	Thank you for your attention and patience,

	Happy New Year,

	Jose Morais







From jjoao at netcabo.pt  Wed Dec 31 11:37:03 2003
From: jjoao at netcabo.pt (Jose Joao Morais)
Date: Fri Apr  8 15:25:38 2005
Subject: [GAP Forum] Tuple attribute
In-Reply-To: <200312310007.hBV07nJT022376@schur.math.colostate.edu>
References: <200312310007.hBV07nJT022376@schur.math.colostate.edu>
Message-ID: <1072870659.4360.25.camel@localhost.localdomain>

Dear GAP Forum,

	About my last question:

	My question is: how can I define a Pair in such a way that it becomes
suitable for all the operations applicable to Tuples?


	I would like to tell you that I've solved the problem for the 'ONE'
operation by defining the following method:


InstallMethod( OneMutable,
        "for pairs",
        true,
        [ IsMultiplicativeElementWithOne and IsPair ], 0,
    function( el )
    local m1, m2;
    
    return(Pair(One(el!.first), One(el!.second)));
end );

	
	Thank you for your attention and patience,

	Happy New Year,

	Jose Morais







From hulpke at math.colostate.edu  Wed Dec 31 19:18:46 2003
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Fri Apr  8 15:25:38 2005
Subject: [GAP Forum] Tuple attribute
In-Reply-To: <1072779925.4368.6.camel@a213-22-130-67.netcabo.pt>
Message-ID: <200312311918.hBVJIkpQ023889@schur.math.colostate.edu>

Dear GAP Forum,

Jose Morais wrote:

> While I hadn't your answer, I implemented a new GAP object (Pair) which
> is in `IsAttributeStoringRep', but I am having difficulties in defining
I still think that keeping tuples and storingthe attribute in the family is
the cleaner and more efficient solution and will save you in the end a lot
of time recoding methods for tuples. 

> My question is: how can I define a Pair in such a way that it becomes
> suitable for all the operations applicable to Tuples?
The easiest is probably to look at the code for tuples (in `tuples.g?') and
duplicate what is done there.

As it might be of interest anyhow, let me add a few remarks about the error
you got:

> InstallMethod( OneOp, "for pairs", true, [ IsPair ], 0,
>
> Error, required filters [ "IsPair" ]
> for 1st argument do not match a declaration of ONE called from

Method installations have to conform to the declaration of the operation,
but one can skip this test by using `InstallOtherMethod' instead (I seem to
recall that there was a similar question recently).

Operations are typically declared in a `.gd' file, but an operation can be
declared several times for different objects (for example the conjugacy
classes of a group or of a character table), and one might have to find the
right declaration.

With `One' (and its derivatives) the situation is complicated further, in
that this is an operation that the kernel must know about (for example for
calculating x^0). The declaration therefore is a bit mor complicated. (The
declaration in basicim.gd you found is a red herring and will only confuse
things -- lets forget about it for the moment.)

Most arithmetic operations (as also `One') are declared in `arith.gd'. (The
comments in this file give much more detail than I can do here.)
We find the following declaration:

  DeclareOperationKernel("OneMutable",[IsMultiplicativeElementWithOne],ONE);

This means: The operation is initially created (under the name `ONE') in the
kernel. (This is needed to have the kernel know about it. Typically
operations that come from the kernel have a kernel name that is all upper
case and then get declared with a ``proper'' library name.)

In our case, `OneMutable' is the library name, but when you type it into
GAP, you still see the kernel name lurking behind:

  gap> OneMutable;
  <Operation "ONE">

(There are other declarations in `arith.gd' (they have essentially to do with
the fact that we might want to store the `One' of a group as an attribute
and -- if the group elements are potentially mutable, as for example
matrices are -- a stored one should be immutable. They all wrap around
`OneMutable'.)

`OneMutable' is declared for the category `IsMultiplicativeElementWithOne'.
To be able to calculate `One' for your pairs, they have to be declared to
be in this category as well. 

This must happen when you declare `IsPair', it is not sufficient that all
pair objects you create are put in this Category.  (As the installation only
is given `IsPair', the method installation does not know about this fact.
You could change the method installation to `IsPair and
IsMultiplicativeElementWithOne', however. In your second mail you state that
this worked. With this, however you might run into the same problem with
other arithmetic operations.)

> I have this definition for pairs:

  BindGlobal( "PairsType",    NewType( PairsFamily, IsPair and
	  IsExtAElement and IsNearAdditiveElement and IsAdditiveElement and
	  IsNearAdditiveElementWithZero and IsAdditiveElementWithZero and
	  IsNearAdditiveElementWithInverse and IsAdditiveElementWithInverse and
	  IsAdditivelyCommutativeElement and
	  CanEasilySortElements and CanEasilySortElements and
	  IsExtRElement and IsExtLElement and IsMultiplicativeElement and
	  IsMultiplicativeElementWithOne and IsMultiplicativeElementWithZero and
	  IsMultiplicativeElementWithInverse and
	  IsAssociativeElement and
	  IsAttributeStoringRep ));

This is the type, which your objects will get. Personally I would leave out
declarations that are anyhow implied (IsMultiplicativeElementWithInverse
implies IsMultiplicativeElementWithOne implies IsMultiplicativeElement
implies IsAssociativeElement, for example)
I also would try to start with only the categories you really need -- for
monoid elements that would be:

IsMultiplicativeElementWithOne (you might want to use
IsMultiplicativeElementWithInverse instead, if you might want to generalize
to groups or if some elements are invertible)

IsPair,
IsAttributeStoringRep, (I suppose `IsPair' implies IsComponentObject')

and -- if you have an efficient comparison implemented (this filter
essentially makes some methods available that rely on elememt comparison)
CanEasilySortElements.

I also would have `IsMultiplicativeElementWithInverse' and
`IsAssociativeElement' to be implied by `IsPair'.

(The reason for leaving out unnecessary declarations is that these might
trigger methods for other kinds of objects which might assume further
properties. The error you got after changing the declaration:
> 	but if I add to these filters 'IsBasicImageEltRep', then, when I try to
> define a pair I get an error:
> Record: '<rec>.Word' must have an assigned value at
is exactly of this kind -- what gets triggered is a `View' method for
`IsBasicImageEltRep' that assumes that a !.Word component is stored in the
object.)

One last remark: If `IsPair' does not imply `IsMultiplicativeElement' and
`IsAssociativeElement' by its declaration, I think you might end up that
sets of pairs (your monoids) will not know automatically to be
`IsMultiplicativeElementCollection' and `IsAssociativeElementCollection' and
thus are not recognized to be semigroups or monoids though your objects all
will multiply fine. 

Best wishes and a Happy New Year,

  Alexander Hulpke

-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke@math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke


From ms8a017 at math.uni-hamburg.de  Tue Dec  9 21:44:34 2003
From: ms8a017 at math.uni-hamburg.de (Hubert Kiechle)
Date: Thu Jan  5 13:04:15 2006
Subject: [GAP Forum] InstallMethod
Message-ID: <Pine.GSO.3.95q.1031209224238.28538A-100000@sun35.math.uni-hamburg.de>

Hi GAP-forum,

I want to invert 2x2 matrices over a (finite) algebra with zero
divisors. As there does not seem to be a method available, I tried to
provide one, but the following file
after *Read*ing into gap leads to the ERROR message below which seems
cryptic to me. In fact, after *return*ing from the break loop
*Inverse* works perfectly well.

How can I get rid of the ERROR message?
Why is there no method for *Inverse* in matrix rings over rings with
zero divisors?


-----  file ----
Inv22:=function(m)
  local  u;
  if DimensionsMat(m)=[2,2] then
    u:=Determinant(m);
    if IsUnit(u) then
      return Inverse(u)*[[m[2][2],-m[1][2]],[-m[2][1],m[1][1]]];
    else 
      return fail;
    fi;
  else
    return fail;
  fi;
end;

InstallMethod( Inverse,
        "Inverse of 2x2 Matrix over any Ring",
        [IsMatrix and IsRingElementCollColl],Inv22);

---------
Error, required filters [ "IS_LIST", "IS_DENSE_LIST", "IS_HOMOG_LIST", 
  "IS_TABLE_LIST", "IsListOrCollection", "IsCollection", "IsExtAElement", 
  "CategoryCollections(IsExtAElement)", 
  "IsNearAdditiveElement", "CategoryCollections(IsNearAdditiveElement)", 
  "CategoryCollections(CategoryCollections(IsNearAdditiveElement))", 
  "IsNearAdditiveElementWithZero", 
  "CategoryCollections(IsNearAdditiveElementWithZero)", 

"CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))", 
  "IsNearAdditiveElementWithInverse", 
  "CategoryCollections(IsNearAdditiveElementWithInverse)", 

"CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))"
    , "IsAdditiveElement", "CategoryCollections(IsAdditiveElement)", 
  "CategoryCollections(CategoryCollections(IsAdditiveElement))", 
  "IsExtLElement", "CategoryCollections(IsExtLElement)", 
  "CategoryCollections(CategoryCollections(IsExtLElement))",
"IsExtRElement", 
  "CategoryCollections(IsExtRElement)", 
  "CategoryCollections(CategoryCollections(IsExtRElement))", 
  "IsMultiplicativeElement", 
  "CategoryCollections(CategoryCollections(IsMultiplicativeElement))", 
  "IsGeneralizedRowVector" ]
for 1st argument do not match a declaration of InverseImmutable called
from
<compiled or corrupted call value>  called from
<function>( <arguments> ) called from read-eval-loop


Thanks for any help,

Hubert

* Priv. Doz. Dr. Hubert Kiechle *
*                               *
* Mathematisches Seminar        *
* Universität Hamburg           *   Outside of a dog,
* Bundesstr. 55                 *     a book is man's best friend.
* D-20146 Hamburg               *   Inside of a dog,
* Germany                       *     it is too dark to read.
*                               *
* Tel.: +49 40 42838 5186       *
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
http://www.math.uni-hamburg.de/home/kiechle/



From kohl at mathematik.uni-stuttgart.de  Wed Dec 10 09:55:02 2003
From: kohl at mathematik.uni-stuttgart.de (Stefan Kohl)
Date: Thu Jan  5 13:04:15 2006
Subject: [GAP Forum] InstallMethod
References: <Pine.GSO.3.95q.1031209224238.28538A-100000@sun35.math.uni-hamburg.de>
Message-ID: <3FD6ED76.DD513B6F@mathematik.uni-stuttgart.de>

Dear Forum,

Hubert Kiechle wrote:

> I want to invert 2x2 matrices over a (finite) algebra with zero
> divisors. As there does not seem to be a method available, I tried to
> provide one, but the following file
> after *Read*ing into gap leads to the ERROR message below which seems
> cryptic to me. In fact, after *return*ing from the break loop
> *Inverse* works perfectly well.
>
> How can I get rid of the ERROR message?
> Why is there no method for *Inverse* in matrix rings over rings with
> zero divisors?
>
> -----  file ----
> Inv22:=function(m)
>   local  u;
>   if DimensionsMat(m)=[2,2] then
>     u:=Determinant(m);
>     if IsUnit(u) then
>       return Inverse(u)*[[m[2][2],-m[1][2]],[-m[2][1],m[1][1]]];
>     else
>       return fail;
>     fi;
>   else
>     return fail;
>   fi;
> end;
>
> InstallMethod( Inverse,
>         "Inverse of 2x2 Matrix over any Ring",
>         [IsMatrix and IsRingElementCollColl],Inv22);
>
> ---------
> Error, required filters [ "IS_LIST", "IS_DENSE_LIST", "IS_HOMOG_LIST",

[ ... ]

The reason for the error message you got is that `InstallMethod' checks
whether the required filters of your method match the declaration of
the attribute `InverseImmutable', for which `Inverse' is a synonym.

You can find these declarations in lib/arith.gd:

   DeclareAttribute( "InverseImmutable", IsMultiplicativeElementWithInverse );
   DeclareSynonymAttr( "Inverse", InverseImmutable );

In your case, the requirement `IsMatrix and IsRingElementCollColl' does not
imply the filter `IsMultiplicativeElementWithInverse' (as there are also non-invertible
matrices), although the attribute `InverseImmutable' is only declared for such
`multiplicative elements with inverse'.

You can circumvent these strict checks by using `InstallOtherMethod' instead of
`InstallMethod'.

In any case you should issue `TryNextMethod();' instead of returning `fail'
in case your matrix is not 2x2 -- otherwise you likely break other functionality,
in particular you might run into trouble when trying to invert matrices larger
than 2x2 after your method installation. This will happen whenever the
method selection ranks your method highest.

You might also think about whether you want to get a mutable or an immutable
result (see the reference manual for a description of mutability / immutability) --
in the former case you should install your method for `InverseMutable',
and in the latter case you should return an immutable object.

Hope this helps,

    Stefan Kohl



From costanti at science.unitn.it  Fri Dec 12 16:52:29 2003
From: costanti at science.unitn.it (Marco Costantini)
Date: Thu Jan  5 13:04:15 2006
Subject: [GAP Forum] The GAP interface to the Singular system
Message-ID: <1071247949.3fd9f24dcd3a8@www.unitn.it>

Dear GAP Forum, 
 
With this message we would like to draw your attention to 
the new version of the GAP interface to the Singular system, 
which has just become available. 
Features of this interface include: 
 
     * fast computation of Groebner bases, 
     * computation of multivariate Gcd, 
     * factorization of multivariate polynomials, 
     * computation of invariant rings of finite groups. 
 
The interface can be downloaded from 
http://www-math.science.unitn.it/~costanti 
 
More information on Singular can be found on 
http://www.singular.uni-kl.de (where the system 
can also be downloaded for free). 
 
If you have any questions please feel free to contact us. 
 
Best wishes, 
 
 
Marco Costantini (costanti@science.unitn.it) 
Willem de Graaf (quagroup@hetnet.nl) 
 
 

From primoz.moravec at fmf.uni-lj.si  Tue Dec 16 16:35:00 2003
From: primoz.moravec at fmf.uni-lj.si (Primoz Moravec)
Date: Thu Jan  5 13:04:15 2006
Subject: [GAP Forum] Low index normal subgroups
Message-ID: <3.0.5.32.20031216173500.00b646e8@fmf.uni-lj.si>

Dear GAP Forum,

what is the best way to compute normal subgroups of low index in a given
finitely presented group?

Best Regards,
Primoz.


------------------------------------
Primoz Moravec
Institute of mathematics, physics
and mechanics
Jadranska 19
SI-1000 Ljubljana
Slovenia

email: primoz.moravec@fmf.uni-lj.si
------------------------------------

From p.dobcsanyi at designtheory.org  Wed Dec 17 11:06:49 2003
From: p.dobcsanyi at designtheory.org (Peter Dobcsanyi)
Date: Thu Jan  5 13:04:15 2006
Subject: [GAP Forum] 'Releases from DesignTheory.org'
Message-ID: <E1AWZVx-0002Ar-00@www.designtheory.org>

            Release Announcements from DesignTheory.org
            ===========================================

The EPSRC funded DesignTheory.org project, based at Queen Mary,
University of London, is pleased to announce the public releases of its
XML-format for block designs and its Design package for GAP.  We expect
these releases to be of interest to those working in combinatorial or
statistical design theory, as well as those interested in the
development of standard electronic formats for mathematical objects.

1)
        The External Representation of Block Designs v1.1,
        http://designtheory.org/library/extrep/

This is a platform independent XML-format for encoding block designs,
and their combinatorial, group-theoretical and statistical properties.

Comments, questions, bug reports -->  extrep@designtheory.org

2)
        Design v1.0 Package for GAP v4.3,
        http://designtheory.org/software/gap_design/

This GAP v4.3 package is for the classification, partitioning and study
of block designs (which include but are not restricted to t-designs).
This package can also write and read block designs in our External
Representation XML-format.

Comments, questions, bug reports -->  gap-design@designtheory.org


Please feel free to forward this announcement to anyone
you think may be interested.

Enjoy,
    The Developers

From costanti at science.unitn.it  Wed Dec 17 14:44:49 2003
From: costanti at science.unitn.it (Marco Costantini)
Date: Thu Jan  5 13:04:15 2006
Subject: [GAP Forum] Low index normal subgroups
In-Reply-To: <3.0.5.32.20031216173500.00b646e8@fmf.uni-lj.si>
References: <3.0.5.32.20031216173500.00b646e8@fmf.uni-lj.si>
Message-ID: <1071672289.3fe06be17b5a6@www.unitn.it>

Dear Primoz and dear gap forum, 
 
Scrive Primoz Moravec <primoz.moravec@fmf.uni-lj.si>: 
> what is the best way to compute normal subgroups of low index in a given 
> finitely presented group? 
 
(I don't know the best way but I can suggest a way to try.) 
 
Look at the functions in the manual in the paragraph Groups - Sets of 
Subgroups: maybe the functions MaximalNormalSubgroups or NormalSubgroups are 
what you need. 
 
Such functions may not terminate in the case that your group is not finite... 
in this case, and if it make sense for your problem, you can consider some 
finite quotient of your group, and calculate MaximalNormalSubgroups or 
NormalSubgroups in it.  
 
There are package to calculare the p-/nilpotent/polyciclic/solvable quotients 
of finitely presented groups (see the packages anupq, nq, etc.). the kind of 
quotient to calculate depends on your problem. 
 
If otherwise your finitely presented group G is finite, it could be better to 
convert it into a polycyclic or permutation group, for efficiency, before 
doing any other computation. 
 
Image(IsomorphismSpecialPcGroup(G));  (if G is solvable) 
Image(IsomorphismPermGroup(G));       (otherwise) 
 
Best Regards, 
Marco 

From hulpke at math.colostate.edu  Wed Dec 17 22:58:47 2003
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Thu Jan  5 13:04:15 2006
Subject: [GAP Forum] Low index normal subgroups
In-Reply-To: <3.0.5.32.20031216173500.00b646e8@fmf.uni-lj.si>
Message-ID: <200312172258.hBHMwlmp016877@schur.math.colostate.edu>

Dear Gap Forum,

Primoz Moravec asked:

> what is the best way to compute normal subgroups of low index in a given
> finitely presented group?

As Marco costatini already pointed out, the methods will be quite different
if you know that the group is finite (``finite'' here probably means: 
order <10^15 ).

If the group is finite, the best approach is to convert to a permutation
group or pc group and use for example `NormalSubgroups'.


If the group is potentially infinite or very large, this might be impossible
or infeasible. In this case I would do the following (assuming again that
your ``small index'' is really small, say up to n=1000:

Using the library of small groups of order <=n (these are the potential
factor groups), determine
- For all solvable groups of order <= n the orders of chief factors. You can
  use these as input to the solvable quotient algorithm to obtain a large
  finite solvable quotient of your group which has all solvable factor
  groups as factors.

- For each nonsolvable group $G$ determine a series of subgroups U1>...>Uk
  such that the image of the action of G on the cosets of Ui is nonsolvable
  and that the action on the cosets of Uk is faithful (often only one
  subgroup suffices, but for groups such as 2.A6 you might want to take a
  subgroup of inder 6 for U1). Then using `LowIndexSubgroups' determine all
  subgroups of the finitely presented group of index $[G:U1]$. Check whether
  the action on the cosets is permutation isomorphic to the action of G on
  the cosets of U1 (for example using `TransitiveIdentification' if the
  index is <=30).
  If U\le F is such a subgroup with [F:U]=[G:U1] determine subgroups of
  index [U1:U2] in U by the low index algorithm. Again compare the types of
  factor groups.
  Iterate until Uk (if not ruled out).

Most nonsolvable groups of large order have a small-degree permutation
representation or a factror group with a low-degree permutation
representation. Thus the second step of this program is probably
comparatively little work.

Best regards,

  Alexander Hulpke

-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke@math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke


From jjoao at netcabo.pt  Tue Dec 30 10:24:49 2003
From: jjoao at netcabo.pt (Jose Joao Morais)
Date: Thu Jan  5 13:04:15 2006
Subject: [GAP Forum] Tuple attribute
Message-ID: <1072779925.4368.6.camel@a213-22-130-67.netcabo.pt>

Dear GAP Forum,

	I have defined an attribute (SemiDirectProductElmAction) for certain
tuples (elements of a semidirect product semigroup being constructed)
because I need to know this attribute to multiply elements of this new
semigroup, but it is not stored when I do

Setter(SemiDirectProductElmAction)(t, act);

	where "t" is the tuple and "act" an action.

	My question is: how can I store this attribute on each of these tuples?


	Thank you,
	Jose Morais


From jjoao at netcabo.pt  Tue Dec 30 10:53:38 2003
From: jjoao at netcabo.pt (Jose Joao Morais)
Date: Thu Jan  5 13:04:15 2006
Subject: [GAP Forum] Tuple attribute
Message-ID: <1072781653.4368.10.camel@a213-22-130-67.netcabo.pt>

Dear GAP Forum,

	I have defined an attribute (SemiDirectProductElmAction) for certain
tuples (elements of a semidirect product semigroup being constructed)
because I need to know this attribute to multiply elements of this new
semigroup, but it is not stored when I do

Setter(SemiDirectProductElmAction)(t, act);

	where "t" is the tuple and "act" an action.

	My question is: how can I store this attribute on each of these tuples?

	Sorry for using the list's old email address, but I got an "Out of
office" reply when sending to the new email address.


	Thank you,
	Jose Morais


From hulpke at math.colostate.edu  Wed Dec 31 00:07:49 2003
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Thu Jan  5 13:04:15 2006
Subject: [GAP Forum] Tuple attribute
In-Reply-To: <1072779925.4368.6.camel@a213-22-130-67.netcabo.pt>
Message-ID: <200312310007.hBV07nJT022376@schur.math.colostate.edu>

Dear GAP Forum,

Jose Morais asked:

>	I have defined an attribute (SemiDirectProductElmAction) for certain
>tuples (elements of a semidirect product semigroup being constructed)
>because I need to know this attribute to multiply elements of this new
>semigroup, but it is not stored when I do

Attributes are only stored if the representation is in
`IsAttributeStoringRep'. Tuples are not in this representation and thus do
not store attributes (which is the behaviour you observed).
To get around the problem there are two ways: the first is to create your
own tuples that use the `ComponentObject' representation and thus are able
to store attributes. In your case however this looks like overkill.

What I would do instead (and is the way similar situations are dealt with in
the library) is to declare the attribute for the *family* of tuples (which
is by default attribute storing):

DeclareAttribute("MyAttribute",IsFamily);

and set this attribute once you create your initial objects:

...
# create generating tuples
tups:=....
fam:=FamilyObj(tups[1]);
SetMyAttribute(fam,actioninfo);

In your multiplication routine (when you need the attribute value) you can
then get it from the family:

MyMultiplication:=function(a,b)
local actioninfo;
  actioninfo:=MyAttribute(FamilyObj(a));

Setter(SemiDirectProductElmAction)(t, act);

(You can see examples of such code in the library file `gprd.gi' that
implements generic products for groups.)

Best wishes and a Happy New Year,

   Alexander Hulpke


-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke@math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke

From jjoao at netcabo.pt  Wed Dec 31 10:47:32 2003
From: jjoao at netcabo.pt (Jose Joao Morais)
Date: Thu Jan  5 13:04:15 2006
Subject: [GAP Forum] Tuple attribute
In-Reply-To: <200312310007.hBV07nJT022376@schur.math.colostate.edu>
References: <200312310007.hBV07nJT022376@schur.math.colostate.edu>
Message-ID: <1072867685.4360.20.camel@localhost.localdomain>

Dear GAP Forum,

	Thank you for your reply to my question about a Tuple attribute.
	While I hadn't your answer, I implemented a new GAP object (Pair) which
is in `IsAttributeStoringRep', but I am having difficulties in defining
a method for the 'ONE' operation applicable to this new object.

gap> p:=Pair(Transformation( [ 1, 2, 3, 4 ] ), Transformation( [ 2, 3,
4, 4 ] ));
Pair(Transformation( [ 1, 2, 3, 4 ] ), Transformation( [ 2, 3, 4, 4 ] ))

gap> Monoid(p);
Error, no method found! For debugging hints type ?Recovery from
NoMethodFound
Error, no 2nd choice method found for `ONE' on 1 arguments called from
OneOp( elm ) called from
One( Representative( M ) ) called from
One( M ) called from
<compiled or corrupted call value>  called from
<compiled or corrupted call value>  called from
...
	

	So, I defined this method:

InstallMethod( OneOp,
        "for pairs",
        true,
        [ IsPair ], 0,
    function( el )
    
    return(Pair(One(el!.first), One(el!.second)));
end );


	but I get the error:

Error, required filters [ "IsPair" ]
for 1st argument do not match a declaration of ONE called from


	Looking then at the declaration of ONE I found:

basicim.gd:210:DeclareOperation( "ONE", [ IsBasicImageEltRep ] );

	
	I have this definition for pairs:

BindGlobal( "PairsType",    NewType( PairsFamily, IsPair and
        IsExtAElement and IsNearAdditiveElement and IsAdditiveElement
and
        IsNearAdditiveElementWithZero and IsAdditiveElementWithZero and
        IsNearAdditiveElementWithInverse and
IsAdditiveElementWithInverse and
        IsAdditivelyCommutativeElement and
        
        CanEasilySortElements and CanEasilySortElements and
        
        IsExtRElement and IsExtLElement and IsMultiplicativeElement and
        IsMultiplicativeElementWithOne and
IsMultiplicativeElementWithZero and
        IsMultiplicativeElementWithInverse and
        IsAssociativeElement and
        IsAttributeStoringRep ));


	but if I add to these filters 'IsBasicImageEltRep', then, when I try to
define a pair I get an error:

gap> p:=Pair(Transformation( [ 1, 2, 3, 4 ] ), Transformation( [ 2, 3,
4, 4 ] ));
Record: '<rec>.Word' must have an assigned value at
return elt!.Word;
 called from
Word( elt ) called from
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop ...


	My question is: how can I define a Pair in such a way that it becomes
suitable for all the operations applicable to Tuples?


	Thank you for your attention and patience,

	Happy New Year,

	Jose Morais







From jjoao at netcabo.pt  Wed Dec 31 11:37:03 2003
From: jjoao at netcabo.pt (Jose Joao Morais)
Date: Thu Jan  5 13:04:15 2006
Subject: [GAP Forum] Tuple attribute
In-Reply-To: <200312310007.hBV07nJT022376@schur.math.colostate.edu>
References: <200312310007.hBV07nJT022376@schur.math.colostate.edu>
Message-ID: <1072870659.4360.25.camel@localhost.localdomain>

Dear GAP Forum,

	About my last question:

	My question is: how can I define a Pair in such a way that it becomes
suitable for all the operations applicable to Tuples?


	I would like to tell you that I've solved the problem for the 'ONE'
operation by defining the following method:


InstallMethod( OneMutable,
        "for pairs",
        true,
        [ IsMultiplicativeElementWithOne and IsPair ], 0,
    function( el )
    local m1, m2;
    
    return(Pair(One(el!.first), One(el!.second)));
end );

	
	Thank you for your attention and patience,

	Happy New Year,

	Jose Morais







From hulpke at math.colostate.edu  Wed Dec 31 19:18:46 2003
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Thu Jan  5 13:04:15 2006
Subject: [GAP Forum] Tuple attribute
In-Reply-To: <1072779925.4368.6.camel@a213-22-130-67.netcabo.pt>
Message-ID: <200312311918.hBVJIkpQ023889@schur.math.colostate.edu>

Dear GAP Forum,

Jose Morais wrote:

> While I hadn't your answer, I implemented a new GAP object (Pair) which
> is in `IsAttributeStoringRep', but I am having difficulties in defining
I still think that keeping tuples and storingthe attribute in the family is
the cleaner and more efficient solution and will save you in the end a lot
of time recoding methods for tuples. 

> My question is: how can I define a Pair in such a way that it becomes
> suitable for all the operations applicable to Tuples?
The easiest is probably to look at the code for tuples (in `tuples.g?') and
duplicate what is done there.

As it might be of interest anyhow, let me add a few remarks about the error
you got:

> InstallMethod( OneOp, "for pairs", true, [ IsPair ], 0,
>
> Error, required filters [ "IsPair" ]
> for 1st argument do not match a declaration of ONE called from

Method installations have to conform to the declaration of the operation,
but one can skip this test by using `InstallOtherMethod' instead (I seem to
recall that there was a similar question recently).

Operations are typically declared in a `.gd' file, but an operation can be
declared several times for different objects (for example the conjugacy
classes of a group or of a character table), and one might have to find the
right declaration.

With `One' (and its derivatives) the situation is complicated further, in
that this is an operation that the kernel must know about (for example for
calculating x^0). The declaration therefore is a bit mor complicated. (The
declaration in basicim.gd you found is a red herring and will only confuse
things -- lets forget about it for the moment.)

Most arithmetic operations (as also `One') are declared in `arith.gd'. (The
comments in this file give much more detail than I can do here.)
We find the following declaration:

  DeclareOperationKernel("OneMutable",[IsMultiplicativeElementWithOne],ONE);

This means: The operation is initially created (under the name `ONE') in the
kernel. (This is needed to have the kernel know about it. Typically
operations that come from the kernel have a kernel name that is all upper
case and then get declared with a ``proper'' library name.)

In our case, `OneMutable' is the library name, but when you type it into
GAP, you still see the kernel name lurking behind:

  gap> OneMutable;
  <Operation "ONE">

(There are other declarations in `arith.gd' (they have essentially to do with
the fact that we might want to store the `One' of a group as an attribute
and -- if the group elements are potentially mutable, as for example
matrices are -- a stored one should be immutable. They all wrap around
`OneMutable'.)

`OneMutable' is declared for the category `IsMultiplicativeElementWithOne'.
To be able to calculate `One' for your pairs, they have to be declared to
be in this category as well. 

This must happen when you declare `IsPair', it is not sufficient that all
pair objects you create are put in this Category.  (As the installation only
is given `IsPair', the method installation does not know about this fact.
You could change the method installation to `IsPair and
IsMultiplicativeElementWithOne', however. In your second mail you state that
this worked. With this, however you might run into the same problem with
other arithmetic operations.)

> I have this definition for pairs:

  BindGlobal( "PairsType",    NewType( PairsFamily, IsPair and
	  IsExtAElement and IsNearAdditiveElement and IsAdditiveElement and
	  IsNearAdditiveElementWithZero and IsAdditiveElementWithZero and
	  IsNearAdditiveElementWithInverse and IsAdditiveElementWithInverse and
	  IsAdditivelyCommutativeElement and
	  CanEasilySortElements and CanEasilySortElements and
	  IsExtRElement and IsExtLElement and IsMultiplicativeElement and
	  IsMultiplicativeElementWithOne and IsMultiplicativeElementWithZero and
	  IsMultiplicativeElementWithInverse and
	  IsAssociativeElement and
	  IsAttributeStoringRep ));

This is the type, which your objects will get. Personally I would leave out
declarations that are anyhow implied (IsMultiplicativeElementWithInverse
implies IsMultiplicativeElementWithOne implies IsMultiplicativeElement
implies IsAssociativeElement, for example)
I also would try to start with only the categories you really need -- for
monoid elements that would be:

IsMultiplicativeElementWithOne (you might want to use
IsMultiplicativeElementWithInverse instead, if you might want to generalize
to groups or if some elements are invertible)

IsPair,
IsAttributeStoringRep, (I suppose `IsPair' implies IsComponentObject')

and -- if you have an efficient comparison implemented (this filter
essentially makes some methods available that rely on elememt comparison)
CanEasilySortElements.

I also would have `IsMultiplicativeElementWithInverse' and
`IsAssociativeElement' to be implied by `IsPair'.

(The reason for leaving out unnecessary declarations is that these might
trigger methods for other kinds of objects which might assume further
properties. The error you got after changing the declaration:
> 	but if I add to these filters 'IsBasicImageEltRep', then, when I try to
> define a pair I get an error:
> Record: '<rec>.Word' must have an assigned value at
is exactly of this kind -- what gets triggered is a `View' method for
`IsBasicImageEltRep' that assumes that a !.Word component is stored in the
object.)

One last remark: If `IsPair' does not imply `IsMultiplicativeElement' and
`IsAssociativeElement' by its declaration, I think you might end up that
sets of pairs (your monoids) will not know automatically to be
`IsMultiplicativeElementCollection' and `IsAssociativeElementCollection' and
thus are not recognized to be semigroups or monoids though your objects all
will multiply fine. 

Best wishes and a Happy New Year,

  Alexander Hulpke

-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke@math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke